Double-pass rotating z-cut quartz plate as a rapidly variable waveplate

We demonstrate a rapidly tunable waveplate based on a rotating z-cut quartz plate in a double-pass configuration. In contrast to previous single-pass implementations, where angular rotation of birefringent crystals causes significant beam path displacement, we show that the double-pass geometry effectively suppresses beam walk-off, reducing lateral shifts to below 10 $\mu$m, which is stable enough to have a fiber coupling. We present a full theoretical description of the polarization changes using Jones matrix calculations and verify it through polarization-resolved measurements. Additionally, the retardation is stable across a broad spectral range without requiring wavelength-specific optimization. When combined with a polarizing beam splitter, the system functions as a high-speed optical power modulator, achieving a dynamic power conversion in 1~ms with its contrast about 1000:1. This compact and robust design is particularly suited for atomic, molecular, and optical (AMO) physics experiments requiring rapid and precise control of light intensity.